Pewne zagadnienia statyki gęstych siatek rusztowych - Klemm, P.; Woźniak, C. (Engineering Transactions, 1969)
The equations of dense and regular surface grid girders, based upon the application of a continuous (fibrous) calculations scheme, were derived in [1]. For grids with perfectly rigid nodes the principal unknowns are the displacements and rotations of the nodes, considered as continuous functions definite upon the surface plane on which the girder grid is formed. If the plane is flat, then the bending of the girder is small in comparison with the height of the cross-section of the beams, and furthermore, one main axis of inertia of each cross-section of each beam is always normal to the plane upon which we are forming the girder grid. In such case, the basic equations and the boundary conditions of the theory lead to two independent boundary problems: one for the displacements and rotations of nodes in the plane of the girder, [2], the other for the displacements and rotations of nodes out of the girder plane, [3]. The above two problems, which can be designated as «disk» and «plate» respectively, have been solved for many cases found in practice; the results of the majority of these works have been collected in the monograph [4]. In this elaboration, however, the general solution is presented for certain plane grid girders, in which the main axes of inertia of the cross-sections of the bars form angles other than ninety degrees with the plane upon which the girder grid is formed. A fragment of one of these grids is illustrated in Fig. 1. In this paper it has been assumed that the grid girders considered constitute linear-elastic systems thereby using only the fully lincarized variant of the equations, Utilizing (1), these equations are compiled in Sec. 1, where the principal designations are also described. The problems comprising the subject of this paper have been restricted to the one-diemnsional problems (grid bands, Sec. 2), presenting for this case in Sec. 3 the form of the general solution. Finally, in Sec. 4 some particular cases are considered, and the results obtained are illustrated with an example in Sec. 5.